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math.DS2019
Iterated function systems with super-exponentially close cylinders
Simon Baker
Several important conjectures in Fractal Geometry can be summarised as follows: If the dimension of a self-similar measure in does not equal its expected value, then t…
math.DS2019
Quantitative recurrence properties for self-conformal sets
Simon Baker, Michael Farmer
In this paper we study the quantitative recurrence properties of self-conformal sets equipped with the map induced by the left shift. In particular, given a function…
math.DS2019
Overlapping iterated function systems from the perspective of Metric Number Theory
Simon Baker
In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approxim…